Graphic Contraction Principle and Applications

A. Petruşel () and I. A. Rus ()
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A. Petruşel: Babeş-Bolyai University of Cluj-Napoca
I. A. Rus: Babeş-Bolyai University of Cluj-Napoca

A chapter in Mathematical Analysis and Applications, 2019, pp 411-432 from Springer

Abstract: Abstract The purpose of this paper is to emphasize the role of the graphic contractions in metric fixed point theory. Two general results about the fixed points of graphic contractions and several related examples are given. The case of non-self graphic contractions will be also considered. Existence, uniqueness, data dependence, well-posedness, Ulam-Hyers stability, and the Ostrowski property for the fixed point equation will be discussed. Some fixed point results in metric spaces endowed with a partial ordering will be also proved. Finally, open questions and research directions are presented.

Keywords: 47H10; 54H25; 47H09; 34D10; 45GXX; 45M10 (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-030-31339-5_15

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DOI: 10.1007/978-3-030-31339-5_15

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